I know a few online servers allow a few variants, but am not aware of places where many variants players would gather, which would they be ?
Are there famous clubs for on the board variants play ?
Collections of fairy chess problems ?
This list of fairy pieces is not at all bad, but could use a few more easy-to-understand diagrams, and some art for representations.
I guess there's enough to say on this topic for books to be published on the subject ?
Unfortunately I don't know of a chess server where they play chess variants, (see update below) but I have a few other resources.
The program Winboard has several variants, including Shogi, Xiangqi, Shatranj and Atomic.
There are also several books written on the subject including:
And the Encyclopedia of Chess Variants
In my ramblings I ran accross this page, indicating that the ICC allows chess variants.
ICC offers a number of chess variants.
I also found a book on Fairy Chess. Unfortunately it appears to be out of print.
I love playing chess variants. For playing live games, FICS supports the major chess variants: Suicide, Atomic, Losers, Crazyhouse and Upside-Down.
For playing correspondence games, I use both Scheming Mind and BrainKing. They each have the normal variants (above), as well as a few unique ones. The ones unique to Scheming Mind include Benedict Chess and Chicken Chess. The ones unique to BrainKing include Ice Age Chess and Cheshire Cat Chess.
These sites are free, for a limited number of games. There are ladders and tournaments, so you can play against other people who enjoy the same variants. You can find me there under my real name (I do not use a handle).
I am surprised that no one yet mentioned http://www.chessvariants.com/ --- the most comprehensive web site on Chess variants I am aware of. They also support a play-by-mail server for many Chess variants.
The Chess variants offer there are range from Modest variants (which is probably close to the variants the original poster is looking for) to rather wild and deviating variant.
You can play correspondence chess variants on the Apronus.com interactive chessboard by generating links to click which encode the board position and all the mvoes made.
For example a short game on an 8x5 board.
animated diagram http://www.apronus.com/chess/moviediagram.php?a=rnbqkbnrHppppppppH8HPPPPPPPPHRNBQKBNR_rnbqkbnrHppppppppH5N2HPPPPPPPPHRNBQKB1R_rnbqkbnrHpppppp1pH5p2HPPPPPPPPHRNBQKB1R_rnbqkbnrHpppppp1pH5P2HPPPPPP1PHRNBQKB1R_rnbqkbnrHpppp1p1pH5p2HPPPPPP1PHRNBQKB1R_rnbqkbnrHpppp1p1pH5P2HPPPP1P1PHRNBQKB1R_rnbqkb1rHpppp1p1pH5n2HPPPP1P1PHRNBQKB1R_rnbqkb1rHpppp1p1pH5n2HPPPPKP1PHRNBQ1B1R_rnb1kb1rHppppqp1pH5n2HPPPPKP1PHRNBQ1B1R&d=MRNBQ_B_RPPPPKP_P_____n__ppppqp_prnb_kb_r0&w=8&h=5/
Try Connect Score. The game combines Chess with Dots and Boxes. The game can be viewed at: http://connect-score.blogspot.ca/
There's a training site on variants : https://chessvariants.training/
We support these variants: Antichess, Atomic chess, King of the Hill, Three-check, Horde chess and Racing Kings.
So more or less the set of variants supported on lichess. It's mostly puzzles about tactics, and some about endgames.